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Pointwise Improvement of Multivariate Kernel Density Estimates

✍ Scribed by Belkacem Abdous; Alain Berlinet

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 428 KB
Volume: 65
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1998.1742

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✦ Synopsis

Multivariate kernel density estimators are known to systematically deviate from the true value near critical points of the density surface. To overcome this difficulty a method based on Rao Blackwell's theorem is proposed. Local corrections of kernel density estimators are achieved by conditioning these estimators with respect to locally sufficient statistics. The asymptotic as well as the small sample size behavior of the improved estimators are studied. Asymptotic bias and variance are investigated and weak and complete consistency are derived under mild hypothesis.

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